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Question
Which of the following statements is true for HCF and LCM of two distinct natural numbers a and b?
- HCF is always greater than LCM.
- HCF is a factor of LCM.
- LCM is a factor of HCF.
Options
(i) only
(i) and (iii)
(i) and (ii)
(ii) only
MCQ
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Solution
(ii) only
Explanation:
(i) HCF is always greater than LCM: False.
The HCF is always less than or equal to the LCM (HCF ≤ LCM).
(ii) HCF is a factor of LCM: True.
Because HCF × LCM = a × b, the HCF must divide the LCM.
(iii) LCM is a factor of HCF: False.
The LCM is a multiple of the HCF, not a factor.
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